LIGHTROOM Catalog should be able to synchronize drives with duplicate files so editing can be done on any of the drives

I would like to have the ability to synchronize multiple drives to a single catalog, so I could edit files on multiple drives and Lightroom's view of any drive would look the same. Currently, I can find NO way of doing this.

You mean you want original photos duplicated on multiple drives, and you want to be able to work from any of them (perhaps a duplicate drive at work and at home)? There are numerous pieces of file synchronization software that would create your duplicate drives, and you could certainly link your catalog to any of these drives at any one time.

I upload RAW files to one external HDD and to a RAID NAS drive. I usually edit files from the external drive. Occasionally I edit files on the NAS. I've imported the files from both drives to LR. If I open one drive I see the files that have been edited there, if I pick the NAS I only see what files I have edited there. I'd like a simple menu option in LR to let me see the edit status of files on both drives.

Drive A file 1 has 2 proofs. If I select Drive A in Library, I'll see a dark border and proof numbers. If I open NAS in Library, I won't see anything except the thumbs of the 'copy' files there. I'd like to see some indication in Library that file 1 has been edited. If I edit file 2 in NAS, and then open Drive A, I want to see file 1 has as a proof and that file 2 has also been edited. If drive A crashes, I want to be able to see and possibly re-edit the copy files on NAS. Would third party software let me do this?

Trying to simplify this...I'm proposing that the catalog should be enhanced so that it becomes a GLOBAL catalog. The editing process is non-destructive. Would it be difficult to link the cataloged XMP file to all the instances of that image file? That way, when selecting a file on any drive the view would be the same for all drives. Using the Library with a global catalog, any edit to one file edits all instances of that file.

Yeah, ok, so I have a similar setup. Taking a simplified overview, I have the image files on my NAS, and the same files are replicated on my local external drive, which is faster. These are kept mirrored using file sync software (Chronosync for Mac - ViceVersa is a Windows equivalent I've used in the past).

The catalog is on the laptop drive. If I'm away from the external drive, I can right-click on the parent folder in LR, choose Update Folder Location or Find Missing Folder, depending on which is visible, and directly it to the NAS. Do the same when I'm back at the desk, linking it to the external drive instead.